One known example of a measurement apparatus comprises a torsion balance that employs the paramagnetic property of a test gas to measure the partial pressure of the test gas which is present in a measurement chamber. A non-uniform magnetic field is applied across a chamber containing a test body. The test body is held by a suspension filament, acting as a torsion spring, so as to allow the test body to have a single degree of rotational freedom. The non-uniform magnetic field causes a disturbing torque to be applied to the test body in the presence of a paramagnetic gas, and this enables the partial pressure of the paramagnetic gas to be measured. Oxygen is one of a small number of naturally-occurring gases that exhibits paramagnetism, and has a stronger magnetic susceptibility than other gases. Paramagnetic oxygen sensors have been used in a number of industrial and medical applications.
In some examples of systems that measure the partial pressure of oxygen, a test body comprises a pair of hollow glass spheres mounted on a rigid bar, the centre of which is mounted on a fine filament that is held under tension and that is perpendicular to the bar. A strong magnetic field gradient is applied across the assembly such that the force acting on each of the spheres creates a disturbing torque that is opposed by the torsional elasticity of the filament (i.e. the disturbing torque moves the test body until balanced by the torque created by the filament held under tension—the filament behaves as a weak torsion spring). A mechanism of this type is described in U.S. Pat. No. 2,416,344.
The force Fm that acts on a spherical test body in an inhomogeneous magnetic field is proportional to its volume V, the magnetic field strength H and gradient dH/dz and the volume magnetic susceptibility difference between the test body X1 and surrounding sample gas X2 (see “The magnetic susceptibility of nitrogen dioxide”, G G Havens, Phys. Rev. vol 41 (1932) pp. 337-344). That is:Fm∞V*H*dH/dz*(X1−X2)
Since the volume magnetic susceptibility of the sample gas is proportional to the sample gas density, the force acting on the test body is proportional to the partial pressure of oxygen. The volume magnetic susceptibility of oxygen at room temperature is 1.9×10−6 SI units, whereas nitrogen (a typical background gas) is −6.7×10−9 SI units. Therefore the force due to oxygen in the gas mixture, even small amounts, is substantially larger than other gas components, hence the excellent selectivity of this measurement principle to oxygen.
The force described above is quite weak, typically a few micro-Newtons with pure oxygen for magnetic field strengths and test body volumes that can be practically achieved. Consequently a very sensitive system is required to measure this force with the resolution typically required for oxygen sensing applications.
The typically preferred arrangement uses a magnetic susceptibility torsion balance inside a sealed cell which includes an inlet to admit the sample gas. The torsion balance comprises a test body filled with a diamagnetic gas (e.g. nitrogen) or an evacuated rigid volume. The body is suspended in a non-uniform magnetic field in the sealed cell, and is typically balanced by initially filling the cell with the same diamagnetic gas that fills the test body. When the cell is subsequently filled with a sample gas containing oxygen, the paramagnetic oxygen gas is attracted to the stronger part of the magnetic field, and the test body rotates. This rotation is detected and used to indicate the oxygen content of the sample gas.
To ensure good linearity and a high level of sensitivity, an electronic optical lever is employed. A light source is reflected from a mirror mounted centrally between the spheres. In early devices, the reflected beam was detected using an optical readout which indicated the degree of displacement. In later developments, the reflected beam is detected using one or more photo detectors, and a controlled electrical current is passed through a conductor wound around the test body substantially perpendicular to the magnetic field in such a way that the torque generated through interaction of the current and the fixed magnetic field acts to oppose the disturbing torque resulting from the paramagnetic gas, to maintain the assembly in a fixed null position. The current required to balance the torsion balance can then be measured in order to determine the disturbing torque resulting from paramagnetic effects, to determine the oxygen content. This modification to the basic mechanism is described in UK patent GB 746,778. Aside from secondary effects, the assembly only permits rotation of the test body around the longitudinal axis of the torsion spring, and inhibits any linear motion of the test body relative to the assembly.
Modern oxygen sensors that require high sensitivity still use the optical lever with refinements (see “Highly accurate measurement of oxygen using a paramagnetic gas sensor”, R P Kovacich, N A Martin, M G Clift, C Stocks, I Gaskin, J Hobby, Measurement Science and Technology, vol 17 (2006), pp. 1579-1585). A solid state source (light emitting diode) is used in place of an incandescent one, alongside a pair of photodiodes connected in reverse polarity to provide a zero voltage null position when both photodiodes are equally illuminated, i.e. when the beam spot centre is exactly in between the photodiodes. Using a pair of photodiodes also has the advantage of rejecting common mode errors, such as intensity fluctuations of the light source. This electronic optical lever feedback system gives much improved sensitivity, linearity and stability.
In sensitive measurement systems, such as the example paramagnetic oxygen sensors described above that use a torsion balance, balancing of the mechanical elements is required. Without this balancing, interaction of the imbalance mass and gravity generates forces (an imbalance torque in the case of the example torsion balance described above) that cause erroneous readings.
In particular, if the centre of mass of the rotating test body is not coincident with its axis of rotation (i.e. the suspension filament acting as a torsion spring in the example described above), changes in tilt or orientation of the assembly will change the torque required to maintain the null position of the test body. Thus, when the spheres and associated structures do not have a centre of mass coincident with the torsion spring, balance weights must be added to move the centre of mass to, or close to, the torsion spring. The cost of accurately balancing the test body can be a significant proportion of its manufacturing cost and minor imbalances may remain.